# Gauss theorem and the nature of the surface

1. Apr 24, 2013

### ananthu

According to Gauss’ law the total number of lines of force over a closed surface is equal to 1/ε times the net charge enclosed within the closed surface. Why should it be a closed surface but not an open surface too? I am unable to find a convincing explanation for it. Since we take into account only the number of lines starting or reaching a charge, the total number of lines is not going to vary whether we take a closed surface or open surface near the charge. Then why should it be specifically a closed one? Can anyone giving a convincing explanation?

2. Apr 24, 2013

### Staff: Mentor

If the surface is open, you can get any arbitrary value. It is important that you enclose the whole mass - without leaks, so to speak.
There is no "number of lines of force".

3. Apr 25, 2013

### ananthu

Thank you for the reply. If there is no lines of force, then how the calculated value of 1.129 x 1011 lines of force from 1 C of charge placed in air or vacuum arrived? What does that number exactly stand for? The value has been obtained from the formula 1/ε for air.

4. Apr 25, 2013

### sz0

I am by means an expert but, what Gaus law does is to collect all that flows through a surface. If you dont totally enclose the charge there will be flow going out that you are not calculating.

5. Apr 25, 2013

### mikeph

Because only a closed surface can enclose a charge.

How do you define "enclosed charge" when your surface is open?

6. Apr 25, 2013

### Staff: Mentor

I have no idea who did that, but it is wrong.
Nothing.
$$\frac{1C}{\epsilon_0}=1.13\times 10^{11} Vm$$
The numerical value depends on the units you use - if you convert this to imperial units, you get a different number, for example. This alone shows that the numerical value itself cannot have a physical meaning (like some number of "lines").

7. Apr 26, 2013

### ananthu

8. Apr 26, 2013

### Staff: Mentor

It is pointless to talk about a "number of lines of force". Such a thing does not exist.
I think "line of force" itself is a problematic concept, but at least it has some clear meaning (=field lines). Let's look at the points 1m away from a charge: Every point is on its own "line of force", and the number of points in a distance of 1m is infinite. There is no way to get any finite number for "lines of force". If you want to draw them, you have to restrict yourself to a finite number, but that is not an exact drawing of the field.